To make the aioli: Beat the yolk with the vinegar and mustard in a bowl. Whisk in the oil, drop by drop, to make a thick mayonnaise
. Squeeze the garlic
out of the roasted cloves
into the mayonnaise and whisk
smooth. Season the aioli with salt, pepper, and lemon juice
, to taste.
To prepare the artichokes: Trim the artichokes, rubbing with lemon as you go, until you are down to the core
with a bit of stem attached. Halve. While you're trimming, bring a pot of water to the boil. Squeeze the juice of a lemon into it and salt it. Drop in the artichokes
and cook until tender, about 10 minutes, depending on the size. Drain, and pat dry. Heat the olive oil in a skillet and brown the artichokes on all sides. Transfer to paper towel to drain
. Serve with the aioli.